Mapping Ocean Observations in a Dynamical Framework:
A 2004-06 Ocean Atlas
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Forget, Gaël. “Mapping Ocean Observations in a Dynamical
Framework: A 2004–06 Ocean Atlas.” Journal of Physical
Oceanography 40.6 (2010) : 1201-1221. Copyright c2010
American Meteorological Society
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http://dx.doi.org/10.1175/2009jpo4043.1
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Mapping Ocean Observations in a Dynamical Framework: A 2004–06 Ocean Atlas
GAËL FORGET
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
(Manuscript received 1 May 2008, in final form 13 March 2009)
ABSTRACT
This paper exploits a new observational atlas for the near-global ocean for the best-observed 3-yr period
from December 2003 through November 2006. The atlas consists of mapped observations and derived
quantities. Together they form a full representation of the ocean state and its seasonal cycle. The mapped
observations are primarily altimeter data, satellite SST, and Argo profiles. GCM interpolation is used to
synthesize these datasets, and the resulting atlas is a fairly close fit to each one of them. For observed
quantities especially, the atlas is a practical means to evaluate free-running GCM simulations and to put field
experiments into a broader context. The atlas-derived quantities include the middepth dynamic topography,
as well as ocean fluxes of heat and salt–freshwater. The atlas is publicly available online (www.ecco-group.
org). This paper provides insight into two oceanographic problems that are the subject of vigorous ongoing
research. First, regarding ocean circulation estimates, it can be inferred that the RMS uncertainty in modern
surface dynamic topography (SDT) estimates is only on the order of 3.5 cm at scales beyond 300 km. In that
context, it is found that assumptions of ‘‘reference-level’’ dynamic topography may yield significant errors (of
order 2.2 cm or more) in SDT estimates using in situ data. Second, in the perspective of mode water investigations, it is estimated that ocean fluxes (advection plus mixing) largely contribute to the seasonal fluctuation in heat content and freshwater/salt content. Hence, representing the seasonal cycle as a simple interplay
of air–sea flux and ocean storage would not yield a meaningful approximation. For the salt–freshwater seasonal cycle especially, contributions from ocean fluxes usually exceed direct air–sea flux contributions.
1. Introduction
Estimates of the oceanic state, whether instantaneous
or averages over varying time intervals, have a variety of
uses. In particular, ‘‘climatologies’’ are meant to represent the long-term mean ocean state. Such climatologies
(e.g., Stephens et al. 2002; Gouretski and Koltermann
2004; Curry 2001) are widely used to initialize and test
model solutions and to describe flows and transports.
Almost without exception, such climatologies are based
upon some form of objective mapping involving weighted
averages of the data in both time and space. Despite their
evident utility, a limitation of these climatologies is that
the mapped temperatures, salinities, and/or derived flows
do not follow from known equations of motion or kinematics. An early attempt to produce time-averaged fields
satisfying known equations was given by Wunsch (1994),
but the methodology was not practical on a global scale.
Corresponding author address: Gaël Forget, Dept. of Earth,
Atmospheric and Planetary Sciences, Massachusetts Institute of
Technology, Cambridge, MA 02139.
E-mail: gforget@mit.edu
DOI: 10.1175/2009JPO4043.1
Ó 2010 American Meteorological Society
Another difficulty with climatologies is the extreme
inhomogeneity in both space and time of the underlying
oceanic sampling [e.g., Forget and Wunsch 2007; Wunsch
et al. (2007) for a discussion of sampling issues]. The recent increase in in situ data coverage due to the advent of
the Argo array is such that, over large fractions of the
ocean, more samples have been collected over the last
few years than over the previous 100 yr (e.g., Forget and
Wunsch 2007). It seems obvious that this dense database
yields relatively robust estimates of the contemporary
ocean state, but it is unclear whether it may yield significant improvements in representing the long-term mean
ocean state (i.e., the ocean climatology). Unless the
temporal bias in data coverage is handled properly, new
climatology estimates may indeed only be remotely representative of the long-term mean ocean state and boil
down to estimates for the few recent years instead. This
issue is clearly illustrated by Fig. 1 showing the mean date
of observation for two hypothetical climatologies—one
computed before the advent of Argo (top panels) and one
computed afterward (bottom panels). The complexity of
Fig. 1’s maps is challenging, even when the recent years’
data are not included (top panels). It suggests a need for
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FIG. 1. Mean date of observation for two datasets, (left) T and (right) S, on average for the upper 1000 m. The mean date of observation
is mapped using the OI procedure described in appendix A, taking 1980 as the first guess. The date of observation map shows the period
that the associated T or S map (produced with OI) would best represent. It depends on the temporal distribution of observations. (bottom)
The dataset consists of the Boyer et al. (2006) observations from 1950 to 2006, complemented with recent Argo observations (up to 2006).
(top) The dataset is restricted to observations between 1950 and 2000.
caution in interpreting in situ climatology estimates as
representations of the long-term mean ocean state in
general. In that respect, the likely temporal bias toward
present-time climatology estimates that include the vast
recent Argo data is of most concern (bottom panels).
Here, the intention is to provide a mean monthly atlas
over the comparatively intensely sampled recent period
2004–06. The result is a simple time average of solutions
to known numerical equations of motion based upon
the Massachusetts Institute of Technology (MIT) GCM
(Marshall et al. 1997; Adcroft et al. 2004). Observational
maps are created by solving for a nonlinear least squares
fit of GCM trajectories to a variety of observations
(listed in Table 1). Spatial interpolation is provided by
the GCM itself, and the underlying time evolutions are
consistent with the model equations. Availability of Argo
data, in particular, motivates the choice of time interval.
The greatly increased data coverage means that this interval should be a suitable reference time against which
to measure future shifts in the oceanic state.
Before presenting the results, we first summarize the
observations employed (section 2) and briefly review the
estimation approach (section 3). Further methodological
details are provided in appendixes at the end of the paper.
Section 4 establishes the reliability of the atlas for observed quantities. Sections 5 and 6 analyze oceanographic
implications of the results. Section 7 concludes the paper.
2. Datasets
The near-global ocean datasets included as constraints in the GCM interpolation problem are (i) Argo
subsurface profiles of temperature (hereafter T) and
salinity (hereafter S); (ii) monthly mapped sea surface
temperature (SST) satellite measurements from infrared sensors (Reynolds and Smith 1994) and microwave
sensors (maps produced by Remote Sensing Systems);
(iii) along-track sea level anomaly measurements by
satellite altimeters (see Table 1); and (iv) mean surface
dynamic topography based on the CLS01 mean sea
surface and the EIGEN-GRACE-03S geoid model (but
no in situ data) provided by M. H. Rio (Rio et al. 2005).
Regional in situ datasets are also included as observational constraints (see list in Table 1). The following
simplifications are used: 1) geoid and altimeter data are
combined to form a single (along track) absolute sea
level constraint; 2) mapped SST data are used as constraints rather than raw pixel SST data; and 3) no sea-ice
data is used as constraint.
An adjusted version of the World Ocean Atlas 2005
(WOA05; Locarnini et al. 2006) climatology for T and S
is also used as part of the GCM interpolation problem,
to constrain regions where Argo does not provide observations (typically below 2000-m depth and over highlatitude ice-covered regions). To avoid encroaching on
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TABLE 1. Summary of datasets that are built into the new atlas. SST stands for satellite-measured sea surface temperature. SLA stands for
satellite altimeter–measured sea level anomaly.
Name
Source
Argo profiles
XBT profiles*
CTD profiles*
Southern Ocean profiles*
Tropical mooring time series*
Infrared SST
Microwave SST
Topex/Poseidon SLA
Geosat Follow-On SLA
Envisat SLA
Surface mean dynamic topography
WOA05–Argo blend
Near-surface atmospheric state
Scatterometer wind stress
Coriolis Argo Data Center
D. Behringer, NCEP
World Ocean Circulation Experiment
Southern Elephant Seals as Oceanographic Samplers (SEaOS)
Tropical Atmosphere Ocean Prediction and Research Moored Array in the Tropical Atlantic
Reynolds and Smith (1994), National Oceanic and Atmospheric Administration (NOAA)
Remote Sensing System
Physical Oceanography Distributed Active Archive Center (PODAAC)
U.S. Navy, NOAA
AVISO
M. H. Rio; see section 2
Locarnini et al. (2006); see section 2
Kalnay et al. (1996), NCEP
PODAAC
* Datasets with fairly regional or sparse data coverage.
the fit to Argo observations elsewhere, WOA05 maps
are adjusted to Argo observations using a univariate
interpolation method (see appendix A).1 The resulting
WOA05–Argo blend is then simply applied as a background constraint everywhere in the GCM interpolation
problem. As Argo data are introduced twice (directly as
profiles and via the WOA05–Argo blend) in the GCM
interpolation problem, other observational constraints
are upweighted by a factor of 2 to maintain a balance
between data types. This least squares upweighting is
omitted in section 4 for simplicity.
The in situ data coverage of the upper ocean (above
2000-m depth) for the period from 2004 to 2006 is illustrated in Fig. 2. Most of the global upper ocean has
been observed during that period, which is largely due to
Argo floats. Hence an atlas for that period may improve
upon (long-term mean) climatologies over most of the
upper ocean. In Fig. 2, the median number of observations per grid point is 3, while 15% of the grid points
show more than 10 observations, and 30% of the grid
points show no observations. Of concern are some relatively wide regions that lack observations altogether,
because they present a particular challenge to ocean
observation by drifting floats [such as sea ice coverage
(e.g., in the Southern Ocean) or topographic obstacles
(e.g., in the Indonesian seas, or near coasts in general)].
Unlike for the majority of the global upper ocean, a
2004–06 atlas may not improve much upon climatologies
in those regions that lack contemporary in situ observations (Fig. 2). The same is true for the entire deep ocean
(below 2000-m depth) that Argo floats do not reach.
1
In this paper, the term ‘‘univariate’’ simply denotes that a
physical quantity is individually estimated, unlike in GCM interpolation.
3. GCM interpolation problem
The constrained least squares problem (formulated in
appendix A) is similar to that solved by Wunsch and
Heimbach (2007). The reader is referred to Wunsch and
Heimbach (2007) for a discussion of the method of Lagrange multipliers used to solve the constrained least
squares problem. As for the latest Estimating the Circulation and Climate of the Ocean (ECCO) Global
Ocean Data Assimilation Experiment (GODAE) estimates (Wunsch and Heimbach 2008), a sea ice model
and a surface atmospheric layer model are included. The
GCM configuration is summarized in appendix B. The
single most important difference compared to Wunsch
and Heimbach (2007, 2008) is a reduction of the estimation interval(s), from 14–16 yr to 16 months here. Each
calculation estimates the oceanic state over one calendar
year plus the previous 4 months, hence covering slightly
more than one seasonal cycle. The results of three such
(overlapping) calculations are time averaged (see appendix A for details) first to form a 3-yr daily time series,
then to form a mean monthly atlas representing an average seasonal cycle for the period from 2004 to 2006. The
resulting atlas is hereafter called the Ocean Comprehensible Atlas (OCCA). The term ‘‘comprehensible’’
denotes that the underlying equations of motion are
known. Unsurprisingly, the shorter estimation interval(s) produce a closer fit to observations than does the
14–16-yr ones used by Wunsch and Heimbach (2007,
2008) (Fig. 3), as initial conditions are more efficient
controls over the shorter period. The reduction of the
estimation interval(s) to 16 months can be thought of as a
practical means to confine model error accumulation [as
explained by Forget et al. (2008b); see also appendix A].
OCCA consists of a set of fields for each month of the
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FIG. 2. Number of in situ samples collected over the period from 2004 to 2006, for (top) T and (bottom) S, per 18 3 18 square and vertical
level, on average in the upper 2000 m.
year. It does not resolve interannual fluctuations. The
underlying 3-yr daily time series may be used to study
those, but this is beyond the scope of this study.
4. The fit to observations
The reliability of OCCA maps for observed quantities
must first be established. OCCA is meant to synthesize
mainly three datasets: Argo profiles, SST data, and altimeter data. For each one, the accuracy of alternative
univariate atlases (due to other research groups) will be
taken as a reference. Formal error estimates are generally
lacking in ocean state estimates, whatever their origin. The
present study is no exception. Although this major issue
must eventually be resolved, it lies beyond the scope of the
present study. Yet in practice, normalized estimate-toobservation distances can be used to crudely compare the
accuracy of various large-scale estimates. This framework
shall first be laid out (next paragraph), then applied to
OCCA and alternative univariate atlases (Figs. 3–8).
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~ as defined in section 4) to Argo profiles for (top) T and
FIG. 3. Normalized distance (J(X);
(bottom) S, averaged over longitude, latitude, and vertical levels (0–2000-m depth range). Here
s
~ is the Forget and Wunsch (2007) estimate. Gray curves are for two recent ECCO GODAE
solutions (Wunsch and Heimbach 2007). The thick and thin black curves are for OCCA (mean
monthly atlas) and for the underlying time series, respectively.
Assume that an ensemble of N observations, {xi, i 5
1, N}, of a quantity X are available with normally distributed noise. Let X~ be an estimate of XT, the true
value of X. Let s
~ be an estimate of sT, the true noise
standard deviation. We can define a normalized estimateto-observation distance as
N
~ 5
J(X)
1
(X~ xi )2 /~
s2 .
N i51
å
N
It is clear that the expected values for 1/N åi51 (X T xi )
N
and 1/N åi51 (X T xi )2 are 0 and sT2, respectively.
2
~ is s 2 /~
It follows that the expected value of J(X)
T s 1
2 2
~
~
s , where X X T is the actual estimate er(X X T ) /~
~ increases with
ror.2 This relation implies that (i) J(X)
the actual estimate error amplitude; (ii) for a given set of
estimates, fX~ j , j 5 1, Kg, the range of J(X~ j ) decreases
~
as the estimated noise level (~
s) increases; and (iii) J(X)
does not simply depend on the number of observations.
In using pointwise measurements to derive large-scale
state estimates, representation error includes eddy signals. The amplitude of eddy signals shows strong spatial
variations so that s
~ must vary in space (e.g., Forget and
2
The ‘‘actual estimate error’’ is not to be confused with a ‘‘formal error estimate.’’
~ would otherwise
Wunsch 2007). Domain averages of J(X)
only represent the most energetic regions. Property 1
~ values a practical method
makes the comparison of J(X)
to compare the accuracy of large-scale estimates, even
though it should not be mistaken for an analysis of formal
errors (that would not behave according to properties 2
and 3). We note that the following analysis could be exs in detail,
tended by examining distributions of (X~ xi )/~
which are largely Gaussian (not shown).
For the subsurface hydrography, OCCA is evaluated
relative to the WOA01 climatology (Stephens et al.
2002), taken as a best-reference estimate of the longterm mean ocean state from pre-Argo observations. We
postpone comparisons to the latest climatology estimates (such as WOA05) that are a blend of recent Argo
data and historical in situ data. It is indeed unclear how
these climatology estimates should be interpreted, since
they may show a large temporal bias toward present
time (see Fig. 1).
Figure 4 shows that OCCA is more consistent with
contemporary Argo profiles than is the WOA01 longterm mean ocean state estimate (Stephens et al. 2002).
This result is encouraging because it suggests that OCCA
reflects some of the ocean state characteristics specific to
the period 2004–06. Unsurprisingly, the biggest differences
~ occur in the Southern Ocean where the climain J(X)
tology is based upon a very thin database (Forget and
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FIG. 4. As in Fig. 3, but for a different set of estimates, and averaged over time (period from
2004 to 2006), longitude and vertical levels (0–2000-m depth range). Black curves: same as in
Fig. 3. Thick gray curves: WOA01 mean monthly climatology (Stephens et al. 2002). Thin gray
curves: Fourier truncated WOA01 (see appendix A).
Wunsch 2007). The full model time series (from which
OCCA is a time average) is marginally closer to the
Argo profiles than is OCCA, which suggests that some
of the model variability that is averaged out upon
moving from the time series to the atlas may be realistic.
A somewhat opposite conclusion arises when Fourier
truncation is applied to smooth the climatology seasonal
cycle (see appendix A for details), which marginally
reduces misfits to Argo profiles. This behavior is thought
to reflect seasonal cycle noise in the original monthly
climatology (see section 6).
Misfits between observations and truly optimal
large-scale estimates ideally should consist of randomly
distributed noise (e.g., with no large-scale or long-term
patches). Relative to a long-term mean climatology such
as WOA01, misfits between OCCA and observations do
usually consist of small-scale noise to a good extent. This
is illustrated for salinity at an intermediate depth in the
Southern Ocean by Fig. 5. At first glance, the differences
in hydrographic structures between the two atlases are
relatively subtle (Fig. 6). One noticeable feature is that
the salinity minimum along the Antarctic Circumpolar
Current (ACC; between 408 and 658S) shows almost the
same value at all longitudes in OCCA, but not in the
climatology. An important question is whether such differences can be attributed to climate fluctuations, which is
left for further investigation.
For sea surface temperature (SST; Fig. 7) and sea level
anomaly (SLA; Fig. 8), comparison of the distances to
observations yields similar conclusions about the respective accuracies of OCCA and WOA01 estimates. Note
that Fig. 8 does not address the annual mean sea level that
will be discussed in section 5. Also, for WOA01, the
seasonal cycle in dynamic height is used as an approximation of the seasonal cycle in SLA. This approximation
was tested for OCCA and makes almost no difference for
~ (not shown). The range of J(X)
~ is the narrowest for
J(X)
bin-averaged along-track SLA observations (Fig. 8) and
the widest for mapped SST data (Fig. 7). This simply reflects (see property 2 above) that the signal-to-noise ratio
K
s2 for the X~ j , j 5 1, K
(defined as (1/K)åj51 (X~ j X t )2 /~
estimates) differs from one dataset to another.
Slightly more insight can be obtained by comparing
~ for OCCA and for satellite atlases. First, for SST, a
J(X)
mean monthly satellite atlas is formed by time averaging
the monthly data provided by Remote Sensing Systems
and Reynolds and Smith (1994). Accuracy of OCCA is
similar to that of this satellite atlas (Fig. 7), reflecting that
OCCA captures most of the SST seasonal cycle. Second,
for SLA, a mean monthly satellite atlas is formed from
Archiving, Validation, and Interpretation of Satellite
Oceanographic data (AVISO)/CLS maps. These maps
synthesize altimeter observations down to the mesoscale (on a 1/ 48 3 1/ 48 mesh). OCCA, however, may only
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FIG. 5. Time-averaged misfit between (top) WOA01 or (bottom) OCCA and Argo profiles collected from 2004 through 2006, for S, at
300 m. Overlaid black contours: annual mean isohalines in OCCA.
effectively resolve signals that span a few grid points on a
18 3 18 mesh. Before comparison with OCCA, AVISO/
CLS maps are smoothed to filter out spatial scales smaller
than 38. The mean monthly satellite atlas is formed by
time averaging these smoothed maps. Consistent with our
large-scale objectives, the accuracy of OCCA is similar to
that of this satellite atlas (Fig. 8).
In summary, OCCA includes accurate maps for observed quantities, synthesizing Argo, SST, and altimeter
data. In resolving the large scales, the accuracy of OCCA
maps is similar to that of univariate maps. The key additional value of the new atlas follows from the inclusion of
dynamical principles, which relate the various fields to
one another. OCCA includes fields not only for observed
quantities but also for many other quantities (e.g., volume, heat, and salt–freshwater fluxes). As part of the
GCM interpolation procedure, all quantities (observed or
otherwise) are made consistent with the full suite of observations. OCCA fields for quantities that are not directly observed may be thought of as derived estimates.
These fields allow for an extended interpretation of observations. The following sections provide examples of
derived estimates and discuss oceanographic implications.
5. OCCA annual mean circulation
The classical problem of determining the ‘‘referencelevel’’ circulation is embedded in GCM dynamics. Previous studies (Forget et al. 2008a,b) have provided evidence
that sets of Argo profiles allow successful inversions for
the barotropic and baroclinic circulations in a GCM
interpolation framework. The focus in this section is on a
few important aspects of the annual mean circulation,
while the following section assesses seasonal fluctuations in the circulation.
a. Surface dynamic topography
In the absence of sufficiently accurate geoid estimates
(Vossepoel 2007), improving estimates of time-mean surface dynamic topography (SDT) remains an outstanding
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FIG. 6. Annual mean salinity map at 300 m in (top) WOA01 and (bottom) OCCA. Overlaid black
contours: annual mean isohalines in OCCA.
issue. By definition, SDT is the difference between sea
surface height and geoid. Many SDT estimates consist
simply of a difference between a time-mean sea surface height estimate and a geoid estimate (hereafter
MSS-geoid estimates). Some recent SDT estimates
(Stammer et al. 2002; LeGrand et al. 2003; Maximenko
and Niiler 2004; Rio et al. 2005; among others), however, employ additional observational and/or dynamical constraints.
The OCCA SDT estimate is thus an adjusted version
of a MSS-geoid estimate provided by M. H. Rio. The
adjustment is obtained, as part of the GCM interpolation procedure, by fitting altimetric and in situ data,
along with the MSS-geoid SDT. Rio et al. (2005) have
also estimated an SDT adjustment by adding altimetric
and in situ data constraints, but using a very different
method. We shall here compare the two estimated adjustments. While computational details are reported in
appendix C, two aspects are worth emphasizing here: (i)
Rio et al. (2005) and this study both start from the same
MSS-geoid, except for changes of reference time periods; (ii) scales smaller than 300 km are filtered out of
both adjustments for comparison purposes.
The two estimated adjustments show RMS values of
3.5 cm (OCCA) and 3.3 cm (Rio et al. 2005). They both
may be regarded as estimates of errors in the MSS-geoid
SDT. Hence we attribute an RMS uncertainty between
3.3 and 3.5 cm to the MSS-geoid SDT at scales beyond
300 km. This inference is consistent with the RMS uncertainty range suggested by Vossepoel (2007), which is
from ’3.5 to ’4.2 cm for MSS-geoid SDT at scales
beyond 334 km (see their Fig. 4). The two adjustments
show fairly contrasting patterns though (Fig. 9), so that
their cross correlation is only 0.3, and this raises suspicion about the details of both adjustments. The RMS
difference between the OCCA SDT and Rio et al.
(2005) adjusted SDT is 4.0 cm, while that between the
OCCA SDT and MSS-geoid SDT is 3.5 cm. We thus
attribute an RMS uncertainty between 3.5 and 4.0 cm to
the OCCA SDT, which is basically the state of the art.
b. Middepth dynamic topography
Under the hydrostatic approximation, dynamic height
(DH) for the layer between the surface and 1600-m
depth (0–1600) equals the difference between surface
dynamic topography and 1600-m dynamic topography
(DT)(1600). These three quantities [i.e., SDT, DT(1600),
and DH(0–1600)] are estimated jointly in OCCA according to geoid and altimeter constraints (of SDT), Argo
constraints (of dynamic height), volume conservation,
and other constraints. As part of the three-term hydrostatic balance, DT(1600) is the term that is less directly
related to observations and may therefore be regarded
as the inverted quantity. Note that inversion using GCM
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FIG. 7. As in Fig. 4, but for mapped monthly (top) microwave and (bottom) infrared SST
data. Mapped microwave SST data are from Remote Sensing Systems. Mapped infrared SST
data are from Reynolds and Smith (1994). Here s
~ is the RMS difference between microwave
and infrared maps (period from 2003 to 2006). Color code is the same as in Fig. 4, but the case of
a satellite atlas is also shown (dashed gray curves). To form the mean monthly satellite atlas,
microwave maps and infrared maps are first averaged together using equal weights; mean
monthly fields are then computed for the period from 2004 to 2006. The dashed gray curves
show the distance between this satellite atlas and the monthly data.
interpolation involves no ad hoc assumption of referencelevel circulation.
The estimated DT(1600) reflects expected middepth
circulation pathways (Fig. 10), including North Atlantic
subpolar gyre recirculations (Lavender et al. 2005) and
Southern Hemisphere subtropical gyres (Davis 2005).
For the Antarctic Circumpolar Current, the estimated
difference in DT(1600) across the current is 47 cm, which
FIG. 8. As in Fig. 7, but for altimeter SLA along-track data [from Ocean Topography Experiment (TOPEX)/Poseidon, Envisat, and Geosat Follow-On (GFO)]. In these computations
~ (i) along-track data are averaged in 18 3 18 daily bins; (ii) time-mean values are
of J(X),
subtracted. Here s
~ is the estimate of Ponte et al. (2007). For WOA01 (solid gray curves), the
seasonal cycle in dynamic height is used as an approximation of the seasonal cycle in SLA. To
form the mean monthly satellite atlas, weekly maps (obtained from AVISO/CLS; DT-MSLA
reference product) are first smoothed to filter small-scale signals (see text); mean monthly fields
are then computed for the period from 2004 to 2006. The dashed gray curves show the distance
between this satellite atlas and the daily bin-averaged altimeter data.
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FIG. 9. Adjustments to MSS-geoid SDT (cm) under in situ constraints (see appendix C for computational
details). (top) From Rio et al. (2005); (bottom) in OCCA.
is a third of the surface value (150 cm).3 Other noteworthy features include widespread midlatitude contrasts
in DT(1600) between oceanic basins: 5 cm between the
Pacific and Atlantic, and 3 cm between the Pacific and
Indian.4 Geostrophic streamlines tend to align along
continental margins in the DT(1600) map, except in
regions of significant vertical motions. In the subpolar
North Atlantic, streamlines appear near margins due to
(well known) high-latitude deep downwelling. In the
subtropical western North Atlantic, streamlines vanish
as the deep southward flow partly upwells toward intermediate depths.
Over the global ocean, DT(1600) shows a standard
deviation of 24 cm, mostly due to ACC and isolated basin
3
Average values between the 152-Sv (1 Sv [ 106 m3 s21) barotropic streamline and the Antarctica shelf.
4
Median values between 408S and 408N.
values. For the region between 408S and 608N and excluding the Mediterranean and the Japan Sea, DT(1600)
shows a standard deviation of 2.2 cm. The magnitude
of DT(1600) contrasts (Fig. 10) is not small compared
with SDT uncertainties and estimated SDT adjustments
(Fig. 9). Hence we conclude that erroneous assumptions
of reference-level circulation, corresponding to the middepth dynamic topography, may seriously undermine
efforts to improve SDT estimates using in situ data.
c. Example of transport estimates
Provided that the large-scale flow is near geostrophic,
observational constraints of the hydrography and surface
dynamic topography can provide efficient constraints
of transports. Lacking direct transport observations, the
new atlas transports can hardly be tested though—only
compared with independent estimates. The emphasis here
is on volume transports for two of the best-documented
sheared flows.
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FIG. 10. Annual mean dynamic topography (cm) at 1600-m depth in OCCA. This quantity is the
pressure anomaly at 1600 m expressed in cm. Regions that are not color shaded are those where the sea
floor is above 1600 m.
The estimated 3-yr mean ACC transport through
Drake Passage is 152 Sv.5 The estimated shear consists
of a 42-Sv cell reversing about 1400-m depth (Fig. 11).
As in previous studies, the flow is now described using
two layers separated by 2500-m depth. The flow in both
layers (140 Sv above 2500 m and 12 Sv below) is slightly
larger than the reference estimate (125 6 10 Sv above
2500 m and 9 6 5 Sv below) of Whitworth and Peterson
(1985) and Whitworth (1983) by about 15%. The estimated ACC variability at Drake Passage (5.7 Sv) is
mostly unsheared, while the reversing cell strength
barely varies (0.9 Sv).6 An eddying Southern Ocean
state estimate (so-called SOSE; M. Mazloff 2008, personal communication) shows a fairly similar mean flow
structure (154 Sv top to bottom, and 55 Sv for the reversing cell) and variability structure (4.8 Sv top to
bottom, and 1.6 Sv for the reversing cell).
At 278N the estimated North Atlantic meridional
overturning rate is 16 Sv.7 It includes a southward contribution of 7 Sv below 3000 m, which is large compared
with unconstrained z-coordinate model solutions (see,
e.g., Willebrand et al. 2001; Forget et al. 2008b). To facilitate comparisons with other observational estimates,
the flow is now decomposed into an ocean interior flow
(between the Bahamas and the Africa shelf) and a
Florida Strait flow. The Florida Strait northward transport (26.5 6 3 Sv) is 20% smaller than cable measurements indicate (31.5 6 3 Sv). The estimated total ocean
5
Top to bottom integrated value.
Values are standard deviation of daily transports.
7
Maximum value of the time-mean overturning streamfunction
at 278N.
6
interior flow compensates the estimated Florida Strait
transport by construction and includes a 3.7-Sv northward Ekman transport. The ocean interior shear consists
of a 9-Sv cell reversing at 500-m depth, with a northward
deep branch (Fig. 12, left). Figure 12 shows that the
geostrophic ocean interior shear in OCCA (12 6 2 Sv) is
20% smaller than the value (15 6 3 Sv) computed from
the Rapid Climate Change (RAPID) mooring data (Fig. 12,
right). A difference in deep geostrophic shear is evident
between the RAPID and OCCA estimates (Fig. 12,
right). A test computation for OCCA (gray curves) shows
that this difference is likely a consequence of the mooring
subsampling. Additional RAPID array data (e.g., over
the mid-Atlantic ridge) might help resolve this issue.
For volume transports (OCCA and others), the above
analysis suggests 20% uncertainties. That figure is merely
an educated guess, however, based upon only two sheared
flows.
d. Concluding remarks
The OCCA estimate of the annual mean ocean circulation is in reasonable agreement with alternative
estimates of dynamic topography and transports. For
transports especially, this result reflects that global observing systems provide efficient constraints of the
density field (Argo, etc.) and of the surface dynamic
topography (altimeters, etc.).
The atlas middepth dynamic topography, DT(1600),
is proposed as a practical means to convert observed
transects of T and S (e.g., along ship tracks) into absolute
geostrophic transport transects. DT(1600) lies well within
the Argo-sampled layer and the flow is already relatively
weak at this depth. By construction, DT(1600) is a solution
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FIG. 11. Time-mean volume transport through Drake Passage cumulated from the bottom
(thick dashed curve), and its decomposition in unsheared flow (thick gray curve) and shear flow
(thick black curve). The unsheared flow equals the depth-averaged velocity at all depths, while
the shear flow is defined as the difference between total flow and unsheared flow. The thin
curves deviate from the thick curves by 3 times the daily value standard deviation.
to the global ocean circulation inverse problem including grid-scale to global conservation principles. Direct
application of DT(1600) as an estimate of geostrophic
reference-level streamfunction is thus a convenient alternative to challenging synoptic inversion procedures.
DT(1600) (section 5b) implies realistic surface dynamic
topography (section 5a) and transports (section 5c)
when it is combined with hydrography observations
(section 4).
6. OCCA seasonal cycle
The real ocean seasonal cycle of heat content (freshwater content) has to balance fluxes of heat (freshwater),
and this dynamical principle is built into OCCA. One of
the interpretations of the GCM interpolation problem is
an attempt to infer air–sea fluxes and ocean fluxes that
are responsible for observed fluctuations (e.g., Stammer
et al. 2004). Let us first provide an overall assessment of
OCCA mean monthly surface fluxes of heat and freshwater. The RMS mean monthly differences between
OCCA and National Centers for Environmental Prediction (NCEP) surface fluxes are shown in the bottom
panels of Fig. 13. These maps are regarded as crude estimates of uncertainties that may equally apply to both
flux estimates (OCCA and NCEP fields). While OCCA
fluxes are adjusted to best fit ocean observations, these
uncertainties (bottom panels) cover a relatively large
fraction of the very fluxes (top panels). Keeping this in
mind, let us then focus on the seasonal fluctuation (i.e.,
deviations from the annual mean) and extend the discussion to inferences of fluxes within the ocean.
a. Implied fluxes
For any monthly hydrographic atlas, the varying flux
divergence that is required to explain the seasonal cycle
of heat and freshwater content can be computed as
appropriately scaled differences between successive
months. We shall refer to the result of this diagnostic
computation as ‘‘implied fluxes,’’ and focus on their
magnitude. This diagnostic computation does not address annual mean fluxes, but only deviations from the
annual mean. We also note that implied fluxes may
equally be attributed to fluxes through the ocean surface
(air–sea fluxes, ice–sea fluxes, and runoff) or fluxes
within the ocean (advection and mixing). In section 6b,
we will distinguish between those two contributions.
The implied fluxes for WOA01 and OCCA are strikingly different: WOA01 usually shows much larger implied fluxes than does OCCA (Fig. 14). It is suggested
hereafter that WOA01 implied fluxes might be too
large because of a lack of observational and dynamical
constraints. It shall not be excluded that OCCA implied fluxes are too small, and further investigation is
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FIG. 12. (left) As in Fig. 11, but for the North Atlantic flow through 278N, between the
Bahamas and the African shelf. The thin curves deviate from the thick curves by one daily
standard deviation. (right) For the geostrophic shear flow (depth-averaged flow set to zero) for
three different estimates: from the OCCA 3-yr time series, using the section of geostrophic
velocity (solid black curves); from the RAPID mooring array data (Cunningham et al. 2007,
their Fig. 1 profiles) for the period from May 2004 through April 2005 (dashed black curves);
from the OCCA 3-yr time series, sampled (at the two basin sides) and processed (thermal-wind
relationship) as for the RAPID array data (gray curves).
suggested on those grounds. Artificially large implied
fluxes might reflect noise in the seasonal cycle, that is,
month-to-month fluctuations inherited from eddy or
instrumental data noise, especially if the database is
thin. Such noise is partly precluded in OCCA because
seasonal fluctuations are imposed by the GCM to occur
gradually as a response to air–sea interactions. Temporal smoothness constraints that are statistical rather than
dynamical can alternatively be added. Fourier series
truncation to the first two annual harmonics is here
chosen and applied to WOA01 (see appendix A for
computational details). This operation largely reduces
implied fluxes (Fig. 14, top and middle panels). A significant degradation of the seasonal cycle estimate
would imply an increase in estimate-to-observation
misfits. However, Fourier truncation tends to reduce
WOA01-to-observation misfits (see section 4). This behavior argues in favor of the smaller implied fluxes
shown by OCCA. For T north of 308S, there is good
agreement in implied fluxes between Fourier truncated
WOA01 (middle) and OCCA (bottom), where they both
rely on a relatively dense database. This result again
argues in favor of the smaller implied fluxes shown by
OCCA. For T south of 308S and for S almost everywhere, Fourier truncated WOA01 still shows much
larger implied fluxes than does OCCA. WOA01 relies
on a thin pre-Argo in situ database there, while OCCA
relies on good coverage by Argo floats, satellite SST,
and altimeters. Except for T north of 308S, Fig. 14 suggests that the pre-Argo in situ database is not sufficient
to estimate accurately the seasonal cycle.
b. Surface versus ocean fluxes
OCCA not only yields implied flux diagnostics, but
also provides detailed estimates of surface fluxes (air–
sea fluxes, ice–sea fluxes, and runoff) and ocean fluxes
(advection and mixing) contributing to the seasonal
cycle of heat and freshwater content. For simplicity,
all advective fluxes (i.e., Eulerian and parameterized
eddy effects) and all diffusive fluxes (i.e., interior and
boundary layer effects) are hereafter presented jointly
as ocean fluxes. Our focus is on splitting the seasonal
cycle of heat and freshwater content into surface and
ocean fluxes.
First, mixed layer budgets are considered, taking the
Southern Ocean as an example. The study of Dong et al.
(2007) provides a reference for heat. There is a satisfactory agreement between OCCA and Argo profiles
for mixed layer depth diagnostics (Table 2). The study of
Dong et al. (2007) and OCCA show remarkably similar
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FIG. 13. (top) RMS mean monthly fluxes through the ocean surface (hereafter S) for (left) heat (W m22) and (right) freshwater
(mm day21) in OCCA. Ocean surface S consists of air–sea fluxes, ice–sea fluxes, and runoff. The dashed line demarcates the region that
experiences sea ice coverage, where RMS(S) largely consists of ice–sea fluxes due to the sea ice coverage seasonal fluctuation. (bottom)
RMS difference between OCCA and NCEP mean monthly surface fluxes. The high-latitude differences largely reflect ice–sea fluxes,
which are omitted in NCEP fields but included in OCCA fields.
mixed layer heat budgets (cf. their Fig. 6a; our Fig. 15
top), despite major differences in parameterizations of
surface and ocean fluxes. Both results show that heat
content tendency and surface fluxes best match each
other in austral winter and spring, whereas ocean fluxes
cause a sizable cooling in austral summer (opposing
warming from the atmosphere). Furthermore, there is a
good quantitative agreement between the two results.
While the previous consistency check for heat is rather
encouraging, OCCA readily allows an extension of the
analysis to salt–freshwater (Fig. 15, right). Unlike for
temperature, surface and ocean fluxes contribute about
equally to the seasonal cycle in mixed layer salinity.
Typically, the mixed layer salinity increases in austral
spring because of ocean fluxes, and decreases in austral
fall because of surface fluxes.
Second, top to bottom integrated budgets are considered (Figs. 16 and 17), following on Fig. 14. For heat
content, surface fluxes (Fig. 16, top left) are only found
to explain most of the seasonal cycle (Fig. 14, bottom
left) in open-ocean subtropical and subpolar regions.
Ocean fluxes (Fig. 16, bottom left) provide major contributions in the tropics and in the vicinity of intergyre
jets. Strikingly for salt–freshwater, ocean fluxes (bottom
right) are found to dominate over surface fluxes (top
right) almost everywhere, except over high-latitude regions that experience sea ice coverage fluctuations.
These results clearly stress the importance of fluctuating
ocean transports in efforts to understand the seasonal
cycle, for most regions.
It should be noted that the maps of Fig. 16 address the
local behavior of the ocean over cells of 18 3 18. Both for
heat and salt–freshwater, surface fluxes usually account
for a larger part of the seasonal cycle budget over wide
regions (Fig. 17, bottom panels) than they do over
18 3 18 cells (top panels). This contrast is observed because fluctuations in air–sea fluxes correlate over wide
regions more than do fluctuations in ocean fluxes.
However, even for wide regions, the seasonal cycle can
only be roughly approximated as a two-term balance
(between storage and air–sea fluxes) for T poleward of
the subtropics (bottom left panel). Even for wide regions, contributions of ocean fluxes to the seasonal cycle
are relatively large for T in the tropics and subtropics,
and for S everywhere (bottom panels).
c. Concluding remarks
The seasonal cycle of heat and salt–freshwater content
in OCCA is consistent with ocean in situ observations
(Argo, etc.) and satellite observations (SST and altimetry). Additional dynamical constraints prevent overfits of
data noise, so that the new atlas does not show large unphysical seasonal fluctuations in T and S (see section 6a).
Unlike univariate maps based on a purely statistical
model, OCCA includes a full budget for the seasonal
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FIG. 14. Magnitude of the flux divergence fluctuation that is implied by the seasonal cycle of the vertically integrated (left) heat (W m22)
and (right) freshwater (mm day21) content, for (top) WOA01, (middle) Fourier truncated WOA01 (see appendix A), and (bottom)
OCCA. The implied fluxes diagnostic computation is kDH/Dtk, where DH is the content difference from one month to the next, Dt is
one month, and double vertical bars stand for standard deviation of mean monthly values. Note that such diagnostics do not reflect
annual mean fluxes, but only the seasonal fluctuation. Contents of T and S are converted to heat and freshwater units by multiplication
with r 3 Cp 5 4000 3 1000 or 1/S0 5 1/35, respectively.
cycle of heat and salt–freshwater content. Hence it provides a physical explanation for the observed seasonality
in heat and salt–freshwater content, which is a combination of surface fluxes (adjusted from NCEP data) and
ocean fluxes (resolved and parameterized physics).
The present data analysis (section 6b) stresses the
importance of fluctuating ocean fluxes, which largely
contribute to the seasonal cycle. Tentative applications
of the new atlas include studies of mode water seasonality and its dynamics. For example, the North Atlantic
Eighteen Degree Water is investigated in separate papers using OCCA (Maze et al. 2009; Forget et al. 2009,
manuscript submitted to J. Phys. Oceanogr.). The OCCA
ocean flux fields might also provide a practical way to
define side boundary conditions in regional models. They
are thought of as a reasonable first guess inferred from
global sets of observations to improve upon thanks to
regional observational efforts.
7. Summary and discussion
This paper exploits a near-global mean monthly ocean
atlas (OCCA) synthesizing a variety of ocean observations for the 3-yr period from December 2003 through
November 2006. OCCA is shown to be acceptably close
to satellite altimeter observations, satellite sea surface
TABLE 2. Correlation between large-scale estimates and Argo
profiles, for the mixed layer depth as defined by Kara et al. (2000,
hereafter KMLD) or de Boyer Montégut et al. (2004, hereafter
BMLD).
KMLD, global
BMLD, global
KMLD, 408–608S
BMLD, 408–608S
OCCA
Time series
OCCA
WOA01
0.89
0.79
0.90
0.80
0.85
0.73
0.87
0.75
0.76
0.60
0.72
0.55
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FIG. 15. Budget over the Southern Ocean mixed layer for (top) T (8C s21) and (bottom) S (salinity s21)
for OCCA (thick curves) and for the underlying time series (thin curves). The budget is simply decomposed as T 5 S 1 O, where T is the tendency (black curves), S are fluxes through the ocean surface
(gray curves), and O is the divergence of fluxes within the ocean (dashed gray curves; advection 1
mixing). Fields of T , S, O are simply volume averaged over the control volume defined by 408S, 608S, the
ocean surface, and the mixed layer depth [computed using the Kara et al. (2000) formula].
temperature data, and in situ Argo profiles. OCCA thus
adequately synthesizes all three datasets. Additional
value of the new atlas follows from the use of a GCM
interpolation framework. First for any individual quantity, observed or otherwise, the atlas takes account of the
whole suite of observations as well as dynamical constraints. A key point is that the additional constraints do
not preclude a close fit to each individual dataset. Second, the various mapped variables are all consistent
with one another according to known dynamical principles, namely a discretized version of the primitive equations. Third, maps of observed quantities are augmented
with derived estimates for quantities that are not directly
observed. These estimates allow for an extended interpretation of observations and additional applications of
the atlas. The atlas is publicly available online (www.
ecco-group.org) and will later be extended beyond 2006.
This paper sheds new light on two oceanographic
problems that are the subject of vigorous ongoing research. First, improving combined estimates of the ocean
circulation and the geoid (e.g., Wunsch and Stammer
2003) remains a challenge. The present analysis suggests
that the RMS uncertainty range for modern geoid estimates ought not to exceed 3.5 cm at scales of 300 km
and more. The results imply that erroneous assumptions
about the deep dynamic topography (or the referencelevel circulation) can yield significant errors of a few
centimeters in combined circulation and geoid estimates.
Second, current field experiments, such as the Climate
Variability and Predictability (CLIVAR) Mode Water
Dynamic Experiment (CLIMODE), aim to refine the
understanding of seasonal cycle budgets. The present
observational synthesis suggests that seasonal fluctuations cannot in general be well approximated as a onedimensional balance between air–sea fluxes and storage
into the ocean. Ocean fluxes (i.e., advection plus mixing)
are found to be key contributors to seasonal cycle budgets, especially for salt–freshwater and for local budgets.
One decisive difference between OCCA and previous
atlases (such as WOA01) is that known dynamics are
accounted for in OCCA. The primitive equations are
indeed encoded in the GCM, which is used as an extensive box model including volume, momentum, and
tracer conservation, and geostrophy has a limit case, etc.
In contrast, ordinary objective mapping relies on a purely
statistical model of the ocean behavior—a time–space
decorrelation model typically. This omission of dynamics
all together is obviously a very crude approximation.
GCMs, while being imperfect, are regarded as refined
approximations compared with decorrelation models.
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FIG. 16. Amplitude of the fluxes that contribute to the seasonal cycle of the vertically integrated (left) heat (W m22) and (right)
freshwater (mm day21) content in OCCA. (top) Part due to fluxes through the ocean surface (kSk) that consist of air–sea fluxes, ice–sea
fluxes, and runoff. The dashed line demarcates the region that experiences sea ice coverage, where kSk largely consists of ice–sea fluxes
due to the sea ice coverage seasonal fluctuation. (bottom) Part due to the divergence of fluxes within the ocean (kOk) that consist of
advection and mixing. Brackets stand for standard deviation of mean monthly values, which implies that annual mean fluxes are omitted
(like Fig. 14, but unlike Fig. 13). These fields may be compared with those in Fig. 14 that show inferences of kT k 5 kS 1 Ok.
A concern with GCMs is that model errors tend to
grow as time evolves, and may grow in convoluted
nonlinear ways. For example, in the North Atlantic,
high-latitude overflow errors are expected to result in
broad midlatitude circulation errors, 3 yr later or so (see
Doscher et al. 1994; Gerdes and Köberle 1995). For that
matter, our pragmatic approach (as in Forget et al.
2008b) is to confine model error growth by stopping integration of the GCM after each seasonal cycle. This
approach readily allows a close fit to observations, which
is the defining quality of an atlas, while imposing dynamics in the seasonal cycle. Model error is thus confined,
even though it is not precluded. A notorious, long-lasting
issue is the Gulf Stream path: many GCM solutions
misplace it, or show a distorted momentum balance
there (see Stammer et al. 2004). The OCCA dynamical
balances may be a reasonable approximation in general,
but there likely are such cases of distorted balances that
will require further refinement.
A common limitation of global ocean atlases is their
time/space resolution. The OCCA atlas consists of mean
monthly fields on a 18 3 18 mesh, implying that sharp
and eddying ocean features can only be represented
in a smooth form. The atlas omits synoptic and smallscale signals, and the fields of Forget and Wunsch (2007)
provide an upper bound estimate for this omission
error for T and S. For that matter and beyond, the
most outstanding issue may be our limited quantitative
understanding of errors. First, estimates of omission–
representation errors need to be refined to better account for synoptic and small-scale signals that global
observing systems do not fully resolve. Second, it is
likely that observing system deficiencies have not yet all
been uncovered, or accounted for in quality control
procedures. Third, errors in ocean, surface layer, sea ice,
etc. models remain poorly understood and accounted
for. Fourth, the extent to which the various ocean state
variables may be retrieved from available observations
largely remains to be elucidated. Along those lines, the
error budget of ocean state estimates, and OCCA specifically, is the subject of an ongoing investigation, which
will be reported elsewhere.
Acknowledgments. Carl Wunsch, Patrick Heimbach,
colleagues at MIT, and the two anonymous reviewers
greatly helped improve this manuscript. This work was
supported by the ECCO GODAE group (www.eccogroup.org), with funding from the National Ocean
Partnership Program (NOPP) and the National Aeronautics and Space Administration (NASA). The Argo
profile data were collected and made freely available by
the International Argo Project (http://www.coriolis.eu.
org). The SEaOS profile data were collected by the
Southern Elephant Seals as Oceanographic Samplers
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FIG. 17. Relative amplitude of the contribution of surface fluxes (S; thick curves) and the
contribution of fluxes within the ocean (O; thin curves) to the seasonal cycle of the vertically
integrated content (T ) of (left) heat and (right) freshwater. Here T , O, and S are defined as in
Fig. 15. (top) Local budgets, showing kSk/kT k and kOk/kT k. (bottom) Zonally integrated
budgets, showing kSk / kT k and kOk / kT k. Overbar stands for zonal average and double vertical
bars stand for standard deviation of mean monthly values.
program (http://biology.st-andrews.ac.uk/seaos/). Microwave OI SST maps are produced by Remote Sensing
Systems (www.remss.com). The CLS/AVISO sea level
products, which were used for comparison purposes,
were produced by SSALTO/DUACS and distributed
by AVISO with support from CNES (http://www.aviso.
oceanobs.com).
APPENDIX A
Interpolation and Averaging Procedures
All interpolation procedures are done within the MIT
GCM ECCO framework (Stammer et al. 2002; Wunsch
and Heimbach 2007). They consist of the minimization
of a least squares distance to observations:
J(x) 5 Jb 1 Jo 5 (x xb )T B1 (x xb )
1 [y(x) yo ]T R1 [y(x) yo ],
(A1)
where x are the adjustable parameters (hereafter control
vector), xb are a prior estimate for x, yo is the observation vector, y(x) are estimate counterparts to yo, and B21
and R21 formally are the inverses of error covariance
matrices. In practice, B is implemented as a covariance
operator using a diffusion operator (after Weaver and
Courtier 2001). This covariance operator is set to favor
large-scale adjustments in x (see below for details). Here
R is a diagonal matrix involving only model–data error
variance estimates (~
s2 using notation in section 4). The
compact y(x) notation may include dynamics (e.g., GCM
time stepping) and interpolation to observed points. We
shall distinguish two levels of complexity.
In the GCM interpolation procedure, x consists of
initial conditions (for T and S) and weekly mean atmospheric state variables (used in bulk formula forcing;
see appendix B), yo includes all observations (from
Argo, altimeters, etc.) and y(x) is the GCM counterpart to yo. The Weaver and Courtier (2001) operator
is set to favor scales of 400 3 cos(f) km and 300 3
cos(f) km (where f is latitude) for initial condition
adjustments and atmospheric variable adjustments, respectively. The GCM adjoint is used to force a least
squares fit of the GCM trajectory to the observation
vector, through iterative adjustments (’30 iterations) of
the control vector.
In a simplified interpolation procedure (hereafter OI),
the very GCM dynamical core is omitted and there is no
time dependency. In this case, y(x) boils down to an
interpolation at observed points and information is only
propagated in space by the B covariance operator. In a
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slightly more complex procedure (hereafter OIF), time
dependency is represented by a Fourier series expansion, and x consists of fields for the various Fourier
coefficients. When using a small number of annual harmonics, OIF yields a smooth seasonal cycle. In both OI
and OIF, each quantity of interest (e.g., the temperature
field) is treated individually. This is in contrast to the
GCM interpolation procedure, where various physical
quantities are coupled through equations of motion and
thermodynamic relations. In OI and OIF procedures,
the Weaver and Courtier (2001) operator is set to favor
scales of 400 3 cos(f) km (f is latitude). The least
squares fit is achieved (iteratively using an adjoint) as for
GCM interpolation.
The OCCA atlas results from applications of the full
GCM interpolation procedure. The initial result consists
of three optimized GCM solutions. Each solution estimates the oceanic state over one calendar year plus the
previous 4 months, hence covering slightly more than one
seasonal cycle. Solutions for two consecutive years have a
4-month overlap period. First, a 3-yr time series is compiled from the three solutions, with a gradual transition
during the overlap period. The gradual transition procedure simply consists of a weighted average of overlapping solutions with time variable weights. The weights
are a 5 (t 2 t0)/(t1 2 t0) and b 5 1 2 a, where t is time, t0
is 1 September, and t1 is 31 December. Second, the time
series is further averaged to produce mean monthly atlas
fields. All atlas fields (temperature, fluxes, mixed layer
depth, etc.) are time averaged in the same way.
The choice to perform three 16-month optimizations
rather than one 3-yr optimization aims at confining
model error accumulation. Given necessarily imperfect
GCM dynamics, one expects spurious GCM drifts. In the
simplest case when model error is linear, the integrated
effect would scale as the experiment duration. For the
purpose of producing a mean monthly atlas, continuous
resolution of the seasonal cycle is important, but continuous resolution of interannual fluctuations is inessential. Confinement of model error is not to be mistaken
for reduction of model error though, which is an important long-term goal beyond the scope of this paper.
The simplified interpolation procedures (OI and OIF)
are applied for various purposes, as mentioned in the
text body. OI is first applied to compute sample mean
date of observation maps shown in Fig. 1. In this case, the
observation vector yo consists of pointwise sample mean
dates computed from the Boyer et al. (2006) dataset and
recent datasets (Argo, XBT, etc.) within 18 3 18 cells.
Second, OIF is applied with two annual harmonics to
smooth the seasonal cycle of the WOA01 and WOA05
atlases. In this case, the observation vector yo consists of
monthly atlas fields (with no other data involved). The
TABLE B1. List of model parameters. Diffusivities in m2 s21.
GM thickness diffusivity
Isopycnal diffusivity
Vertical diffusivity
Horizontal friction
Vertical friction
Quadratic bottom drag
1000
1000
1025
104
1023
0.002
result for WOA01 is referred to as Fourier truncated
WOA01 in the article body. Third, and for WOA05 only,
OI is applied to adjust the annual mean fields to best fit
in situ observations over the period from 2004 to 2006.
The same is done for the two annual harmonics using
OIF. In this case, the observation vector yo consists of in
situ observations (Argo, XBT, etc.) of temperature or
salinity. The result is referred to as WOA05–Argo blend
in section 2 and Table 1.
APPENDIX B
General Circulation Model Setup
The general circulation model is the MIT GCM
(Marshall et al. 1997; Adcroft et al. 2004) and its adjoint
is obtained by automatic differentiation (Giering and
Kaminski 1998; Heimbach et al. 2005). Aside from the
core ocean dynamics, the present experiments include a
bulk formula atmospheric surface layer scheme (Large
and Yeager 2004) and a sea ice thermodynamic model
(Hibler 1980) as implemented in the MIT GCM.
The near-global model domain extends from 808S to
808N, has a resolution of 18 in the horizontal, 50 levels
in the vertical, and a 1-h time step. The model setup uses
a third order upwind advection scheme, an Adam–
Bashforth explicit time stepping, along with an implicit
scheme for vertical diffusion. The model setup uses hydrostatic and Boussinesq approximations, and a linear
implicit free surface. For subgrid-scale process parameterizations, the model setup includes KPP vertical
mixing (Large et al. 1994), GM eddy thickness diffusivity (Gent and Mcwilliams 1990), vertical and isopycnic tracer diffusivity, vertical and horizontal friction, and
a quadratic bottom drag (coefficients listed in Table B1).
The model uses free-slip side boundary conditions and
no-slip bottom boundary conditions. The bulk formulas’
scheme handles freshwater as a virtual salt flux. The bulk
formula atmospheric state variable inputs are air temperature, specific humidity, wind velocity, shortwave
downward flux, and precipitation. Six-hourly atmospheric
state variables from the NCEP reanalysis are used as a
starting point.
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APPENDIX C
Dynamic Topography Computations
Two estimates of time-mean surface dynamic topography from the Rio et al. (2005) study are used here: (i) an
estimate including in situ information (hereafter SDTRio)
for the 1993–99 period (hereafter dT1 period) that is
distributed by CLS (http://www.cls.fr); (ii) an estimate not
) for
including in situ information (hereafter SDTnoinsitu
Rio
the 1993–2004 period (hereafter dT2 period) that was
provided to the ECCO GODAE group by M. H. Rio.
SDTRio is only used for discussion (in section 5a), while
is also part of the GCM interpolation probSDTnoinsitu
Rio
are based on the CLS01
lem. Both SDTRio and SDTnoinsitu
Rio
mean sea surface and the EIGEN-GRACE-03S geoid.
to account for
SDTRio is an adjusted version of SDTnoinsitu
Rio
in situ data (see Rio et al. 2005). Formation of the OCCA
atlas involves an analogous adjustment estimated in a
different framework.
To compare the two adjustments (in section 5), complication arises from different choices of the reference
period (dT1 or dT2) for the SDT itself and for sea level
anomaly (SLA) data. Essentially, dT1 is the CLS standard and dT2 is the ECCO GODAE standard, and a
necessary correction is computed as
dMSS 5 SLACLS
dT2
SLACLS
dT1
,
where SLACLS is the weekly mapped multimission SLA
obtained from AVISO/CLS (DT Maps of Sea Level
dT
Anomaly (MSLA) reference product), and SLA denotes the time average of SLA over dT. The adequate
Rio et al. (2005) SDT adjustment is then computed as
1 dMSS
DSDTRio 5 SDTRio SDTnoinsitu
Rio
and can equally be associated with dT1 or with dT2.
For the new atlas, the analogous adjustment is computed as
DSDTOCCA 5 SDTOCCA SDTnoinsitu
Rio
SLACLS
dT3
1 dMSS,
where SDTOCCA is the OCCA time-mean dynamic topography estimate for the (dT3) period from 2004
to 2006. The third term on the right-hand side is the
CLS estimate of the time-mean anomaly over dT3 refdT3
dMSS) is the same
erenced to dT1. Then (SLACLS
anomaly but referenced to dT2, and finally SDTOCCA dT3
dMSS) is an estimate of the SDT over
(SLACLS
.
dT2 that we compare to SDTnoinsitu
Rio
Aside from the reference period issue, both DSDTRio
and SLACLS are smoothed in space to allow comparisons
VOLUME 40
with the new atlas (sections 4b and 5a). Using a diffusion
operator, scales smaller than 300 3 cos(f) km (i.e., three
GCM grid points) are filtered out, since the GCM cannot
properly resolve these scales. While this smoothing simply is convenient for comparison purposes, we have no
reason to doubt the MDTRio or AVISO maps’ skill at
smaller scales.
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